SOLUTION: For each problem, write a system of equations in two or three variables. Use the method of your choice to solve each system. One night the manager of the Sea Breeze Motel rent

Algebra ->  Linear-equations -> SOLUTION: For each problem, write a system of equations in two or three variables. Use the method of your choice to solve each system. One night the manager of the Sea Breeze Motel rent      Log On


   

Question 271094: For each problem, write a system of equations in two or
three variables. Use the method of your choice to solve each
system.
One night the manager of the Sea Breeze Motel rented
5 singles and 12 doubles for a total of $390. The next night
he rented 9 singles and 10 doubles for a total of $412.
What is the rental charge for each type of room?
Found 2 solutions by unlockmath, stanbon:
Answer by unlockmath(1688) About Me  (Show Source):
You can put this solution on YOUR website!
Hello,
Let x represent singles and y be doubles room. From this we can make two equations.
5x+12y=390
9x+10y=412
Now multiply the first equation by -9 and the second equation by 5 to get:
-45x-108y=-3510
45x+50y=2060
Now we can add these to get:
-58y=-1450 Divide each side by -58 to get:
y=25 Plug this answer into the first equation to solve x:
5x+300=390 Subtract 300 from both sides and divide it by 5 to get:
x=18
There we go. $18 for single and $25 for double. Pretty cheap rent, huh?
RJ
A new book might help you out:
www.math-unlock.com

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
One night the manager of the Sea Breeze Motel rented
5 singles and 12 doubles for a total of $390. The next night
he rented 9 singles and 10 doubles for a total of $412.
What is the rental charge for each type of room?
-----------------------------------------------------
Equations:
5s + 12d = 390
9s + 10d = 412
---------------------
Multiply 1st by 9 ; Multiply 2nd by 5
45s + 108d = 9*390
45s + 50d = 5*412
----------------------
Subtract the 2nd from the 1st and solve for "d":
58d = 1450
d = $25 (rental rate on doubles)
----
Substitute into 5s + 12d = 390 to solve for "s":
5s + 12(25) = 390
5s = 90
s = $18 (rental rate on singles)
========================================
Cheers,
Stan H.